Question

If A (2, 3) maps to A' (4, 6) under a certain enlargement, find the center and scale

factor of enlargement.full step pls

Answer 1

The image A'(4, 6) is the result of dilation of the original point A(2, 3) by a scale factor 2 with a center at the origin.

Therefore, we conclude that If A (2, 3) maps to A' (4, 6) under a certain enlargement:

• The center = (0, 0)

• Scale factor = 2

Explanation:

We know that when any object is dilated by a certain scale factor, it gets reduced or enlarged. The reduction or enlargement depends upon the scale factor.

If the scale factor > 1, the image is an enlargement.

If the scale factor < 1, the image is reduced.

For example, if a point P(x, y) is dilated by a scale factor of 2 with a center at the origin, the image P' will have the coordinates (2x, 2y).

As scale factor 2 > 1, so the image P' is enlarged.

Given the point

A(2, 3)

Rule of dilation by a scale factor 2 with a center at the origin

P(x, y) → P'(2x, 2y)

A(2, 3) → A'(2(2), 2(3)) = A'(4, 6)

It is clear that image A' has the coordinates (4, 6). i.e. A'(4, 6).

In other words, the image A'(4, 6) is the result of dilation of the original point A(2, 3) by a scale factor 2 with a center at the origin.

Therefore, we conclude that If A (2, 3) maps to A' (4, 6) under a certain enlargement:

• The center = (0, 0)

• Scale factor = 2